Question: $92$ people attended a baseball game. Everyone there was a fan of either the home team or the away team. The number of home team fans was $153$ less than $4$ times the number of away team fans. How many home team and away team fans attended the game?
Explanation: Let $x$ equal the number of home team fans and $y$ equal the number of away team fans. The system of equations is then: ${x+y = 92}$ ${x = 4y-153}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${4y-153}$ for $x$ in the first equation. ${(4y-153)}{+ y = 92}$ Simplify and solve for $y$ $ 4y-153 + y = 92 $ $ 5y-153 = 92 $ $ 5y = 245 $ $ y = \dfrac{245}{5} $ ${y = 49}$ Now that you know ${y = 49}$ , plug it back into ${x = 4y-153}$ to find $x$ ${x = 4}{(49)}{ - 153}$ $x = 196 - 153$ ${x = 43}$ You can also plug ${y = 49}$ into ${x+y = 92}$ and get the same answer for $x$ ${x + }{(49)}{= 92}$ ${x = 43}$ There were $43$ home team fans and $49$ away team fans.